[CodesInChaos]

The gravity field of a spherical object only depends on its mass and not its density/radius. So for the Roche limit only the density/radius of the object at risk of breaking apart (called minor object on wikipedia) (earth) should matter, not the one of the major object (black hole).

Wikipedia gives the formula d=R_m*(2m_M/m_m)^{1/3} which matches that intuition.

[semi-extrinsic]

Ah, you're right.

So plugging in numbers you get 2.15 times the radius of Earth, which becomes 13 750 km.

For comparison, Earth-Moon distance is approx. 400 000 km.

[perl4ever]

Yes, but you don't have to be within the Roche limit to have substantial tidal effects, which could destroy habitability at a much greater distance. Just look at Io.